In recent years, in order to perform CT examination in which, a radiation exposure dose is small, image reconstruction has been performed according to a successive approximation method in which an image with less noise even in a small dose can be obtained.
PTL 1 discloses an update formula used for a separable paraboloidal surrogate method (SPS method) which is one kind of the successive approximation method as expressed in Equation (1).
                              μ          j                                                            ⁢                          (                              n                +                1                            )                                      =                              μ            j                                                                      ⁢                              (                n                )                                              -                                                    ∑                                                                  ⁢                                                      γ                    ij                                    ⁡                                      (                                                                  y                        i                                            -                                              ∑                                                                                                  ⁢                                                                              a                            ik                                                    ⁢                                                                                                          ⁢                                                      μ                            k                                                          (                              n                              )                                                                                                                                            )                                                              +                              β                ⁢                                  ∑                                                                          ⁢                                                            w                      jk                                        ⁢                                                                                  ⁢                                          ϕ                      ⁡                                              (                                                                              μ                            j                                                                                                                                                      ⁢                                                              (                                n                                )                                                                                                              -                                                      μ                            k                                                                                                                                                      ⁢                                                              (                                n                                )                                                                                                                                    )                                                                                                                                                d                j                            +                              2                ⁢                β                ⁢                                  ∑                                                                          ⁢                                                            w                      jk                                        ⁢                                                                                  ⁢                                                                  ω                        ψ                                            ⁡                                              (                                                                              μ                            j                                                                                                                                                      ⁢                                                              (                                n                                )                                                                                                              -                                                      μ                            k                                                                                                                                                      ⁢                                                              (                                n                                )                                                                                                                                    )                                                                                                                                                    (        1        )            
In Equation (1), μ is an updated pixel value, y is an original projection value, β is a normalization, coefficient, d is a standardization coefficient, w is a pixel coefficient, i is a detected element number, j and k are pixel number, and n. is the number of times of repetition, In addition, γ is an element of a matrix for converting a projection value into a pixel value, a is an element of a matrix for converting a projection value into a pixel value, Σγij indicates a back projection process, and Σaij indicates a forward projection process. A linear component of a substitute function Ψ of a potential function (also referred to as penalty term) is indicated by ϕ, and a quadratic component thereof is indicated by ω.